Extending deck around a tree

Hello I have a question about surrounding a large maple tree in my back yard with treated deck. Last year I built the deck to within about 6-8 feet of the tree on two sides. It's built on treated 4x4 posts sunk in concrete. Unfortunately I found out as the summer progressed that despite the proximity and the size of the tree (70-80 ft tall), very little of my deck is shaded because its on the south and west sides of the tree which are exposed to afternoon sunlight almost completely at my latitude in Illinois.

So I'd like to continue around the tree this year to add a naturally shaded area of the deck. I understand how to frame the beams and joists around the tree with cross braces and diagonal boards etc. The problem I'm having is designing the base. This is a very large maple with roots near the surface and I was unable to dig any holes deeper than about a foot (frost line is 36 inches here) within 6-8 feet of the trunk. At the minimum this would leave me with a beam span of like 10-12 feet which seems far to long to provide adequate support. I also am leery of being too rough with these roots as I certainly don't want to threaten the health of the tree.

So I'm looking for some ideas of the best way to "float" a couple of posts close to the base of the tree to help bridge the gap. Most importantly I don't want to damage the roots so I can't sink anything very deep, but I also want something as solid as possible that isn't going to rise or sink in a few years...